Question

A convex lens of focal length 'F' produces a real image 'n' times the size of the object. The image distance is

• A. $F(n + 1)$
• B. $F(n - 1)$
• C. $\frac{F}{n+1}$
• D. $\frac{F}{n-1}$

Hint:

A highly useful shortcut formula connecting magnification and focal length directly for lenses is $$m = \frac{F}{F + u}$$or in terms of image distance, $$m = \frac{F - v}{F}$$ . Plugging in $m = -n$ into the second version gives $-n = 1 - \frac{v}{F} \implies \frac{v}{F} = n + 1 \implies v = F(n+1)$ in a single step!

Answer 1

The Correct Option is A

Step 1: Set up the magnification.
Magnification is $m=\frac{v}{u}$. A real image from a convex lens is inverted, so $m=-n$, giving $u=-\frac{v}{n}$.

Step 2: Use the lens equation.
$\frac{1}{v}-\frac{1}{u}=\frac{1}{F}$. Put in $u=-\frac{v}{n}$: \[ \frac{1}{v}+\frac{n}{v}=\frac{1}{F} \]

Step 3: Solve for $v$.
$\frac{1+n}{v}=\frac{1}{F}$, so $v=F(n+1)$. \[ \boxed{F(n+1)} \]